Score: <1 point> Week 5 Correlation and Regression 1. Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.) a. Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)? b. Place table here (C8): c. d. 2 Looking at the above correlations - both significant or not - are there any surprises -by that I mean any relationships you expected to be meaningful and are not and vice-versa? e. <1 point> Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables are significantly related to Salary? To compa? Does this help us answer our equal pay for equal work question? Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Midpoint, age, performance rating, service, gender, and degree variables. (Note: since salary and compa are different ways of expressing an employee's salary, we do not want to have both used in the same regression.) Plase interpret the findings. Ho: The regression equation is not significant. Ha: The regression equation is significant. Ho: The regression coefficient for each variable is not significant Ha: The regression coefficient for each variable is significant Note: technically we have one for each input variable. Listing it this way to save space. Sal SUMMARY OUTPUT Regression Statistics Multiple R 0.99155907 R Square 0.9831894 Adjusted R Square 0.98084373 Standard Error 2.65759257 Observations 50 ANOVA df Regression Residual Total SS MS F Significance F 6 17762.3 2960.383 419.15161 1.812E-036 43 303.70033 7.062798 49 18066 Standard Coefficients Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -1.74962121 3.6183677 -0.483539 0.6311665 -9.046755 5.54751262 -9.0467550427 5.547512618 Midpoint 1.21670105 0.0319024 38.13829 8.66E-035 1.15236383 1.28103827 1.1523638283 1.2810382727 Age -0.00462801 0.0651972 -0.070985 0.943739 -0.1361107 0.1268547 -0.1361107191 0.1268546987 Performace Rating -0.05659644 0.0344951 -1.640711 0.1081532 -0.1261624 0.01296949 -0.1261623747 0.0129694936 Service -0.04250036 0.084337 -0.503935 0.6168794 -0.2125821 0.12758138 -0.2125820912 0.1275813765 Gender 2.420337212 0.8608443 2.811585 0.0073966 0.68427919 4.15639523 0.684279192 4.156395232 Degree 0.27553341 0.7998023 0.344502 0.7321481 -1.3374217 1.88848848 -1.3374216547 1.8884884833 Note: since Gender and Degree are expressed as 0 and 1, they are considered dummy variables and can be used in a multiple regression equation. Interpretation: For the Regression as a whole: What is the value of the F statistic: What is the p-value associated with this value: Is the p-value <0.05? Do you reject or not reject the null hypothesis: What does this decision mean for our equal pay question: For each of the coefficients: Intercept What is the coefficient's p-value for each of the variables: Is the p-value < 0.05? Do you reject or not reject each null hypothesis: What are the coefficients for the significant variables? Midpoint Age Perf. Rat. Service Gender Degree Using only the significant variables, what is the equation? Is gender a significant factor in salary: If so, who gets paid more with all other things being equal? How do we know? <1 point> 3 Salary = Perform a regression analysis using compa as the dependent variable and the same independent variables as used in question 2. Show the result, and interpret your findings by answering the same questions. Note: be sure to include the appropriate hypothesis statements. Regression hypotheses Ho: Ha: Coefficient hyhpotheses (one to stand for all the separate variables) Ho: Ha: Place D94 in output box. Interpretation: For the Regression as a whole: What is the value of the F statistic: What is the p-value associated with this value: Is the p-value < 0.05? Do you reject or not reject the null hypothesis: What does this decision mean for our equal pay question: For each of the coefficients: Intercept What is the coefficient's p-value for each of the variables: Is the p-value < 0.05? Do you reject or not reject each null hypothesis: What are the coefficients for the significant variables? Using only the significant variables, what is the equation? Compa = Is gender a significant factor in compa: If so, who gets paid more with all other things being equal? How do we know? <1 point> 4 <2 points> 5 Midpoint Age Perf. Rat. Service Gender Degree Based on all of your results to date, Do we have an answer to the question of are males and females paid equally for equal work? If so, which gender gets paid more? How do we know? Which is the best variable to use in analyzing pay practices - salary or compa? Why? What is most interesting or surprising about the results we got doing the analysis during the last 5 weeks? Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our sala What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test? ary equality question? ID Salary Compa Midpoint Age 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 66.1 25.9 35.2 55.3 49.6 78.3 42.3 22.8 78 23.3 23.6 60.8 40.6 21.7 21.8 37.4 57 33.5 23 36 76 43.7 25.3 48.9 25.8 23.3 42.3 75.2 80.9 49 24.2 27.5 63.6 28.6 22.4 23.6 24.3 63 34.8 24.3 42.8 23 75.4 60.7 57.9 62.2 62.2 70.1 61.7 61.4 1.159 0.834 1.135 0.971 1.033 1.168 1.058 0.990 1.164 1.014 1.025 1.067 1.014 0.943 0.949 0.934 1.000 1.081 1.000 1.162 1.135 0.911 1.098 1.019 1.122 1.013 1.057 1.122 1.208 1.020 1.054 0.886 1.115 0.922 0.976 1.026 1.057 1.105 1.123 1.057 1.071 0.998 1.125 1.065 1.206 1.091 1.091 1.230 1.083 1.077 57 31 31 57 48 67 40 23 67 23 23 57 40 23 23 40 57 31 23 31 67 48 23 48 23 23 40 67 67 48 23 31 57 31 23 23 23 57 31 23 40 23 67 57 48 57 57 57 57 57 34 52 30 42 36 36 32 32 49 30 41 52 30 32 32 44 27 31 32 44 43 48 36 30 41 22 35 44 52 45 29 25 35 26 23 27 22 45 27 24 25 32 42 45 36 39 37 34 41 38 Performance Service Gender Raise Degree Gender Rating 1 85 80 75 100 90 70 100 90 100 80 100 95 100 90 80 90 55 80 85 70 95 65 65 75 70 95 80 95 95 90 60 95 90 80 90 75 95 95 90 90 80 100 95 90 95 75 95 90 95 80 8 7 5 16 16 12 8 9 10 7 19 22 2 12 8 4 3 11 1 16 13 6 6 9 4 2 7 9 5 18 4 4 9 2 4 3 2 11 6 2 5 8 20 16 8 20 5 11 21 12 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 5.7 3.9 3.6 5.5 5.7 4.5 5.7 5.8 4 4.7 4.8 4.5 4.7 6 4.9 5.7 3 5.6 4.6 4.8 6.3 3.8 3.3 3.8 4 6.2 3.9 4.4 5.4 4.3 3.9 5.6 5.5 4.9 5.3 4.3 6.2 4.5 5.5 6.3 4.3 5.7 5.5 5.2 5.2 3.9 5.5 5.3 6.6 4.6 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 M M F M M M F F M F F M F F F M F F M F M F F F M F M F M M F M M M F F F M F M M F F M F M M F M M Gr E B B E D F C A F A A E C A A C E B A B F D A D A A C F F D A B E B A A A E B A C A F E D E E E E E The ongoing question that the weekly assignments w Note: to simplfy the analysis, we will assume that job The column labels in the table mean: ID - Employee sample number Salary - S Age - Age in years Performan Service - Years of service (rounded) Gender - 0 Midpoint - salary grade midpoint Raise - pe Grade - job/pay grade Degree (0= Gender1 (Male or Female) Compa - s will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? bs within each grade comprise equal work. Salary in thousands nce Rating - Appraisal rating (employee evaluation score) 0 = male, 1 = female ercent of last raise = BS\\BA 1 = MS) salary divided by midpoint